Which angles below are complementary?

Answer: x= 1/2

Step-by-step explanation:

The lengths of the major and minor axis of the ellipse, \( \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}\) are;

An ellipse describes the locus of a point on a curve, such that the sum of the distance from two focal points from the points on the curve is a constant.

The given given function of the ellipse can be presented as follows;

\( \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}\)

The above equation can be compared to the standard equation of an ellipse as follows;

\( \displaystyle{ \frac{ {(x - h)}^{2} }{ {b}^{2} } +\frac{ {(y - k)}^{2} }{ {a}^{2} } = 1}\)

Where;

(h, k) = The coordinates of the center of the ellipse

a = The length of the semi major axis

b = The length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2•√6

b = √(12) = 2•√3

The length of the major axis = 2•a

The length of the minor axis = 2•b

The length of the major axis is therefore;

2•a = 2 × 2•√6 = 4•√6

The length of the minor axis is therefore;

2•b = 2 × 2•√3 = 4•√3

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Answer:

factor of 3

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?

A. (-6, 0)

B. (0, -6)

C. (0, 2)

D. (2, 0)

The graph of the question is attached.

Answer:

The point is (x, y) = (0, 2)

The correct option is C.

Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.

Step-by-step explanation:

From the given graph, the points A and B are

\((x_1, y_1) = (-2, 4) \\\\(x_2, y_2) = (2,-8) \\\\\)

The slope of the equation is given by

\(m_1 = \frac{-8 - 4 }{2 -(-2)} \\\\ m_1 = \frac{-12 }{2+2} \\\\m_1 = \frac{-12 }{4} \\\\m_1 = -3 \\\\\)

We know that the slopes of two perpendicular lines are negative reciprocals of each other.

\(m_2 = - \frac{1}{m_1}\)

So the slope of the other line is

\(m_2 = \frac{1 }{3} \\\\\)

Now we can find the equation of the line that is perpendicular to the line AB and passes through the point C.

From the graph, the coordinates of point C are

\((x_1, y_1) = (6, 4)\)

The point-slope form is given by,

\(y - y_1 = m(x -x_1)\)

Substitute the value of slope and the coordinates of point C

\(y - 4 = \frac{1 }{3} (x - 6)\\\\\)

To get the y-intercept, substitute x = 0  

\(y - 4 = \frac{1 }{3} (0 - 6) \\\\y - 4 = \frac{-6 }{3}\\\\y - 4 = -2\\\\y = 4 -2 \\\\y = 2 \\\\\)

So, the point is

\((x, y) = (0, 2)\)

The correct option is C.

Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.

Answer:

C (0, 2)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

1885

Step-by-step explanation:

Volume = Base x Height

Answer:

10

Step-by-step explanation:

0.35/x=0.035

x=0.35/0.035

 =10

\( \frac{0.35}{x} = 0.035\)

\(0.035x = 0.35\)

\(x = \frac{0.35}{0.035} \)

\(x = 10\)

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the answer

155

324

5/9 (87/3(1/12)= 155/324

The standard form of the equation is y² = 40x.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Here, we have

Given : Focus: (10,0); Directrix: x= -10

Let P = (x,y) be the point on the parabola.

PA = PB, directrix= x + 10 = 0

= √(x - 10)² + y² = |x+10|/√1

= (x - 10)² + y² = (x + 10)²

= (x + 10)² -  (x - 10)² = y²

= 4 × x × 10 = y²

40x = y²

Hence, the standard form of the equation is y² = 40x.

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Answer:

The answer is D, $50.09

Answer:

Step-by-step explanation:

The starting equation is

12-(3x+13)=0

First add 3x+13 to both sides so that only 12 is on the left

12=3x+13

now subtract 13 from both sides to isolate your variable

-1=3x

Finally divide both sides by 3 to get your final answer

x=-1/3

Answer:

15

Step-by-step explanation:

trust me

Answer: 5 plus 2 times 10=25

Step-by-step explanation:

Answer:

The answer is C(t)=0.07t+20

Step-by-step explanation:

20 is the starting value, or y-intercept in this case. The rate of change is 7 cents, or, 0.07. If we put this in y=mx+b format, it will come out as:

C(t)=0.07t+20

The area of a triangle with sides a = 20, b = 15, and c = 25 is 150.

The sides of the triangle are given as a = 20, b = 15, and c = 25.

We will use Hero's formula to find the area of this triangle.

It is a three-face polygon that consists of three edges and three vertices.

We use Heron's formula to find the area of a triangle with 3 sides:

Herons formula:

Area of a triangle =  \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Where a, b, and c are sides of a triangle.

And s = semi perimeter of a triangle.

s = \(\frac{a+b+c}{2}\)

If the sum of two sides of a triangle is greater than the third side of a triangle then the sides of a triangle are true.

Let the given sides be:

a = 20, b = 15 and c = 25.

(20 + 15) > 25

(20 + 25) > 15

(15 + 25) > 20 so the given sides are true.

Now,

Semi perimeter of the triangle:

s = (a+b+c) / 2

s = (20+15+25) / 2

s = 60 / 2

s = 30

Putting s = 30 in the area of the triangle.

we get,

Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\\\)

Area of the triangle = \(\sqrt{30(30-20)(30-15)(30-25)}\\\\\sqrt{30\times10\times15\times5}\\\\\sqrt{22500}\\\\150\)

Thus, the area of a triangle is 150.

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Based on the AA Similarity Theorem, triangles PQR and TSR are proven to be similar to each other because they have two pairs of corresponding angles that are congruent to each other.

The AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. This means that the corresponding sides of the triangles are in proportion to each other.

With the information given, the proof that shows that the two triangles are similar as as follows:

Statements                                         Reasons                                        

1. ∠QPR ≅ ∠STR                                1. Given

2. QR ⊥ PT                                         2. Given

3. ∠QRP ≅ ∠SRT                               3. def. of perpendicular

4. ΔPQR ~ ΔTSR                                4. AA Similarity Theorem

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Answer:

275.46

Step-by-step explanation:

She has $325.31

she writes a check for $24.85

she withdrew $40

and deposited $15

so do 325.31-24.85-40+15

and that equals

275.46

The correct answer is A. The null hypothesis is rejected in error.

In statistical hypothesis testing, a Type II error occurs when the null hypothesis is incorrectly retained or failed to be rejected when it is actually false.

In other words, a Type II error happens when the researcher concludes that there is no significant difference or relationship between variables when, in reality, there is.

It is a false negative result, as the researcher fails to detect a true effect or relationship.

Option A accurately describes Type II error, while the other options are not related to Type II error.

Option B refers to rejecting the research hypothesis, which is not a Type II error but rather a Type I error.

Option C refers to the study being underpowered, which may increase the likelihood of both Type I and Type II errors but is not a direct description of Type II error.

Option D mentions double-blinding, which is a methodological consideration and not directly related to Type II error.

Option E refers to accepting the research hypothesis in error, which is not a Type II error but rather a correct decision or Type I error.

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The required ratio of  is (a + c) : c 11:8.

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have \(a=\frac14 b$\). From the second ratio, we have \(c=\frac{2}{3}b$\). Substituting these values into the expression (a+c):c, we get:

\($$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$\)

Simplifying the expression inside the parentheses, we get:

\($\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$\)

Therefore, the ratio \($(a+c):c$\) is:

\($(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$\)

Hence, the required ratio is 11:8$.

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It means 3 km in 1 minutes.

I think this is a speed of an object which shows that it can run or walk 3km in 1 minutes.

hope you understand.

False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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ANSWER:

STEP-BY-STEP EXPLANATION:

We can calculate the equation of the line using the two blue dots.

The equation in its slope-intercept form is as follows:

To calculate the slope, we need to identify the blue points that would be: (0, 3) and (7, 7)

We calculate the slope as follows:

We already know the y-intercept because it is explicit in the graph and it is (0,3), therefore b is 3, we substitute and the equation would be:

Answer:

i got -2

Step-by-step explanation:

1 step; 8*x-5-(11)=0

2 step; 8x - 16  =   8 • (x - 2)

3 step;  Solve :    8   =  0

4 step; Solve  :    x-2 = 0

final part  Add  2  to both sides of the equation :  

                     x = 2

The height of the trapezoid is 65.5 centimeters.

What is trapezoid ?

A trapezoid, also known as a trapezium in some countries, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs.

The area of a trapezoid is given by the formula:

Area = (1/2) × (sum of bases) × height

Let h be the height of the trapezoid. We are given that the longer base is 131 cm and the shorter base is 85 cm. We are also given that the area is 7,074 square centimeters. Plugging in these values, we get:

7,074 = (1/2) × (131 + 85) × h

Simplifying, we get:

7,074 = (1/2) × 216 × h

Multiplying both sides by 2, we get:

14,148 = 216h

Dividing both sides by 216, we get:

h = 65.5

Therefore, the height of the trapezoid is 65.5 centimeters.

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Answer:

y = -2x - 3

Step-by-step explanation:

Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2

y-intercept= 5 - (-2)(-4) = 5 - 8 = -3

The planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

(a) Desired margin of error = $500

The formula for the sample size required to estimate the population mean with a desired margin of error is:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)

σ = population standard deviation

E = desired margin of error

Since we don't have the actual population standard deviation, we can estimate it using the planning value.

Range of expected salaries = $55,400 - $42,000 = $13,400

Planning value for standard deviation = Range / 4 = $13,400 / 4 = $3,350

Substituting the values into the formula:

n = (1.96 * $3,350 / $500)² ≈ 45.96

Since we can't have a fraction of a sample, we need to round up to the nearest whole number.

Therefore, the sample size needed for a desired margin of error of $500 is 46.

(b) Desired margin of error = $200

Using the same formula:

n = (1.96 * $3,350 / $200)² ≈ 565.44

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $200 is 566.

(c) Desired margin of error = $100

Using the same formula:

n = (1.96 * $3,350 / $100)² ≈ 2,261.76

Rounding up to the nearest whole number, the sample size needed for a desired margin of error of $100 is 2,262.

(d) Would you recommend trying to obtain the $100 margin of error? Explain.

Obtaining a margin of error as low as $100 would require a sample size of 2,262. While this larger sample size may provide a more precise estimate, it also increases the cost and time required for data collection and analysis. Therefore, the decision to obtain such a small margin of error should be based on the practicality and resources available. It is important to consider the trade-off between the desired level of precision and the associated costs and efforts.

Therefore, the planning value for the population standard deviation is estimated to be $3,350, and sample sizes of approximately 46, 566, and 2,262 would be needed to achieve desired margins of error of $500, $200, and $100, respectively.

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Answer:

Step 1

-4 x -3 does not equal -12.

Answer:

The random variable \(\bar x\) has approximately a normal distribution because of the central limit theorem.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n ≥ 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

\(\mu_{\bar x}=\mu\)

And the standard deviation of the sample means is given by,

\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)

Let the random variable X be defined as the age of cars owned by residents of a small city.

It is provided that:

μ = 6 years

σ = 2.2 years

n = 400

As the sample selected is too large, i.e. n = 400 > 30, according to the central limit theorem the sampling distribution of the sample mean (\(\bar x\)) will be approximately normally distributed.  

True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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A closed circuit is required to carry current. If there is a break anywhere in the path, the circuit will open and no current will flow, and the metal atoms in the wire will quickly become peaceful and electrically neutral.

Current flows in a closed circuit, but electrons are left behind in an open circuit.

Imagine a gallon of water flowing through an open pipe. Water flows for a short time, but stops when all the water comes out of the pipe. If you pump water into a closed system of pipes, it will continue to flow as long as you force it to move.

Closed circuit design:

breaks are often created by design. For example, a simple light switch opens or closes the circuit that connects the light to the power source. When building a circuit, it is recommended that the battery or other power source be disconnected when the circuit is not in use. Technically, this creates an open circuit. The

extinguished flashlight is an open circuit. In the flashlight shown here, the flat black button on the bottom left controls the internal switch. A switch is nothing more than two flexible metal strips in close proximity to each other. Push the black button all the way to the right to open the switch and turn off the flashlight. The switch in the open position disconnects the bulb from the battery, creating an open circuit.So, for the light bulb in a circuit turn on when the switch is closed.

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Answer:

$519.79

Step-by-step explanation:

The formula is:

\(PV = P (\frac{1 - ( 1 + r ) ^{-n}}{r})\)

\((100+x)\frac{(1+\frac{0.04}{4})^{40}-1 }{\frac{0.04}{4} }(1+\frac{0.04}{4})^{40}\)  \(+100\frac{(1+\frac{0.04}{4})^{40}-1 }{\frac{0.04}{4} }=50000\)

\((100+x)(\frac{(1+0.01)^{40} -1}{0.01}) (1+0.01)^{40}\) \(+(100)(\frac{(1+0.01)^{40} -1}{0.01} )=50000\)

(100+x) [(1.488864 - 1) / 0.01] (1.488864) + (100) [(1.488864 - 1) / 0.01] = 50000

(100+x) [(0.488864 / 0.01)] (1.488864) + (100) (0.488864 / 0.01) = 50000

(100+x) (48.8864) (1.488864) + (100) (48.8864) = 50000

(100+x) (48.886373) (1.488864) + 4888.64 = 50000

(100+x) (72.785161) + 4888.64 = 50000

7278.5161 + 72.785161 x + 4888.64 = 50000

12167.1561  + 72.785161 x  = 50000

72.785161 x  = 50000 - 12167.1561  

72.785161 x  = 37832.8439

x = 37832.8439 / 72.785161

x = 519.787871

x = $519.79